Dipole moment Fermi resonance

The ACF of the dipole moment operator of the fast mode may be written in the presence of Fermi resonances by aid of Eq. (10). Besides, the dipole moment operator at time t appearing in this equation is given by a Heisenberg equation involving the full Hamiltonian (225). The thermal average involved in the ACF must be performed on the Boltzmann operator of the system involving the real... 

In the presence of Davydov coupling and Fermi resonances, the ACF of the dipole moment operator of the fast mode involving both direct and indirect dampings and also damping of the bending modes, has the same structure as Eq. (272), that is,... 

Thus far, this contribution has been concerned mainly with the energies of vibrational transitions. Intensities were considered only in connection with Fermi resonance and RR spectroscopy. In this section a few short comments about the intensity of vibrational bands in normal IR and Raman spectra are presented. The intensity depends on the electronic stnicture of the species, since changes in the dipole moment (dfi) and in the polarizability (da) during a vibration are caused by changes in the electron density. 

Infrared investigation22 in the p(C=0) region of 2-formyl- and 2-acetyltellurophenes seems to confirm the results obtained using the dipole moment method, but the results are dubious, since the possibility of Fermi resonance was not excluded. 

Let us analyze how the Fermi resonances can be treated within the VPT2 approach, making use of both the variational and perturbative models. In the VPT2 approach, when the harmonic frequencies related to different modes are close to each other, singularities occur in Eqs. 10.16, 10.17, 10.18, and 10.27. Such singularities are usually classified as Fermi type 1 and type 2, corresponding to the conditions 2 or. cOj and -F cOj os. coj, respectively. In the expression of the transition dipole moment for the fundamentals (Eq. 10.27) another type of singularity also occurs when the harmonic frequencies of two fundamental... 

The coupling of the unpaired electrons with the nucleus being observed generally results in a shift in resonance frequency that is referred to as a hyperfine isotropic or simply isotropic shift. This shift is usually dissected into two principal components. One, the hyperfine contact, Fermi contact or contact shift derives from a transfer of spin density from the unpaired electrons to the nucleus being observed. The other, the dipolar or pseudocontact shift, derives from a classical dipole-dipole interaction between the electron magnetic moment and the nuclear magnetic moment and is geometry dependent. 

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